Finite Group Databasebeta

← #25019356

Subgroups — #25019356

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582756C211yesmaximal, characteristic
2C2×#14582746C211yesmaximal, characteristic
3C2×#95×D43C211yesmaximal, characteristic
4#19132854C211yesmaximal, characteristic, complemented
5#19132852C211yesmaximal, characteristic, complemented
6#19132851C211yesmaximal, characteristic, complemented
7#19132820C212yesmaximal, complemented
8#19132819C212yesmaximal, complemented
9(C2×D43)⋊#95C212yesmaximal
10(C2×D43)⋊#95C212yesmaximal
11C43×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×C4×Dic43C2212yes—
19#14582756—24no—
20#14582746C418yescomplemented
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32#95×D43—24no—
33C22×C4⋊C4×C43C2211yescharacteristic
34C2×#95×C43C2212yes—
35C2×#95×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—22no—
45C22×C4×D43—22no—
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—24no—
51C22×C4×D43—24no—
52C22×C4×D43—42no—
53C22×C4×D43—42no—
54C22×C4×D43—42no—
55C22×C4×D43—42no—
56C22×C4×D43C2×C414yes—
57C22×C4×D43D414yes—
58C22×C4×D43Q814yes—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—42no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4C2×C418yes—
67C2×C4×Dic43—42no—
68C2×C4×Dic43—42no—
69C2×C4×Dic43C2×C418yescomplemented
70C43⋊#95—22no—
71C43⋊#95—24no—
72C43⋊#95—22no—
73C43⋊#95—22no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—42no—
78C43⋊#95—42no—
79C43⋊#95—42no—
80C43⋊#95C2×C414yescomplemented
81C23×C4×C43C2312yes—
82C23×C4×C43C2312yes—
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43—22no—
87C2×C4⋊C4×C43—42no—
88#95×C43—22no—
89#95×C43—24no—
90#95×C43—42no—
91#95×C43C2×C414yescomplemented
92C24×C43C2411yescharacteristic
93C23×D43—21no—
94C23×D43—21no—
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43C22×C412yes—
100C23×D43C2×D412yes—
101C23×D43C2×Q812yes—
102C23×D43#4114yes—
103C23×D43#4114yes—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43C22×C414yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×Q812yes—
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43C22×C414yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C2×D412yes—
159C22×Dic43C2×Q812yes—
160C22×Dic43#4112yes—
161C22×Dic43#4112yes—
162C2×C4×D43—28no—
163C2×C4×D43—28no—
164C2×C4×D43—48no—
165C2×C4×D43—44no—
166C2×C4×D43—44no—
167C2×C4×D43—48no—
168C2×C4×D43—48no—
169C2×C4×D43—48no—
170C2×C4×D43—48no—
171C2×C4×D43—48no—
172C2×C4×D43—44no—
173C2×C4×D43—44no—
174C2×C4×D43—44no—
175C2×C4×D43—44no—
176C2×C4×D43C4⋊C4116yes—
177C4⋊C4×C43—44no—
178(C2×D43)⋊C4—216no—
179(C2×D43)⋊C4—48no—
180C4⋊Dic43—44no—
181C4×Dic43—48no—
182C23×C43C23×C411yescharacteristic
183C23×C43C22×D411yescharacteristic
184C23×C43C22×Q811yescharacteristic
185C23×C43C2×#4112yes—
186C23×C43C2×#4112yes—
187C23×C43C2×#4111yescharacteristic
188C23×C43C2×#4111yescharacteristic
189C23×C43C2×#4111yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C43H(5,𝔽2)12yes—
192C23×C43H(5,𝔽2)12yes—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—24no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—24no—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—24no—
209C22×D43—24no—
210C22×D43—24no—
211C22×D43C2×C4⋊C414yes—
212C22×D43#11718yes—
213C22×D43#12414yes—
214C22×D43#12414yes—
215C22×D43#12518yes—
216C2×C4×C43—24no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43C2×C4⋊C414yes—
245C2×Dic43—24no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C4⋊C414yes—
274C4×D43—416no—
275C4×D43—416no—
276C4×D43—416no—
277#13966—431nomaximal, Sylow
278C22×C43C22×C4⋊C411yescharacteristic
279C22×C43C2×#11712yes—
280C22×C43C4×#4111yescharacteristic
281C22×C43C4×#4111yescharacteristic
282C22×C43#51812yes—
283C22×C43#52511yescharacteristic
284C22×C43#52511yescharacteristic
285C22×C43C2×#12411yescharacteristic
286C22×C43C2×#12411yescharacteristic
287C22×C43C2×#12512yes—
288C22×C43#53311yescharacteristic
289C22×C43#53311yescharacteristic
290C22×C43#53411yescharacteristic
291C22×C43#53411yescharacteristic
292C22×C43#54312yes—
293C22×C43#55112yes—
294C22×C43#55112yes—
295C22×C43#55112yes—
296C22×C43#55112yes—
297C22×C43#55312yes—
298C22×C43#55312yes—
299C22×C43#55312yes—
300C22×C43#55312yes—
301C2×D43—24no—
302C2×D43—24no—
303C2×D43—28no—
304C2×D43—28no—
305C2×D43—24no—
306C2×D43—24no—
307C2×D43—24no—
308C2×D43—28no—
309C2×D43—28no—
310C2×D43—24no—
311C2×D43#38218yes—
312C4×C43—24no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—44no—
316C4×C43—82no—
317Dic43—24no—
318Dic43—42no—
319Dic43—42no—
320Dic43—44no—
321Dic43—82no—
322C2×#380—431no—
323C2×C4×C22⋊C4—431no—
324C22×#95—431no—
325#1442—431no—
326#1442—431no—
327#1442—431no—
328#1442D4311yescharacteristic, complemented
329#1434—432no—
330#1434—432no—
331C22⋊#95—432no—
332C22⋊#95—432no—
333C2×C43C2×#38211yescharacteristic
334C2×C43#229611yescharacteristic
335C2×C43#231511yescharacteristic
336C2×C43#235312yes—
337C2×C43#235312yes—
338C2×C43#256111yescharacteristic
339C2×C43#256111yescharacteristic
340C2×C43#256912yes—
341C2×C43#256912yes—
342C2×C43#259111yescharacteristic
343C2×C43#259111yescharacteristic
344D43—28no—
345C24×C4—431no—
346C24×C4—431no—
347C24×C4—431no—
348C22×C4⋊C4—431no—
349C22×C4⋊C4C2×D4311yescharacteristic
350C22×C22⋊C4—432no—
351C22×C22⋊C4—432no—
352C22×C42—432no—
353#380—864no—
354C4×C22⋊C4—438no—
355C2×#95—431no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—431no—
360C2×#95—431no—
361C2×#95—432no—
362C2×#95—431no—
363C2×#95—432no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—864no—
367C2×#95C2×D4312yes—
368C2×#95C2×D4311yescharacteristic
369C2×#95C2×D4312yes—
370C2×#95C2×D4311yescharacteristic
371C43#1396611yescharacteristic, complemented, Sylow
372C25—431no—
373C23×C4—431no—
374C23×C4—434no—
375C23×C4—434no—
376C23×C4—434no—
377C23×C4—432no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—432no—
381C23×C4—862no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—862no—
385C23×C4—864no—
386C23×C4—864no—
387C23×C4—862no—
388C23×C4—862no—
389C23×C4—1722no—
390C23×C4—1722no—
391C23×C4—1722no—
392C23×C4—1722no—
393C23×C4C22×D4312yes—
394C23×C4C22×D4312yes—
395C23×C4C22×D4311yescharacteristic
396C23×C4C22×D4311yescharacteristic
397C23×C4C22×D4311yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—1722no—
402C2×C22⋊C4—438no—
403C2×C22⋊C4—864no—
404C2×C22⋊C4—864no—
405C2×C22⋊C4—864no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—864no—
408C2×C42—438no—
409C2×C42—1722no—
410C2×C42—1722no—
411#95—22no—
412#95—24no—
413#95—42no—
414#95—434no—
415#95—864no—
416#95—864no—
417#95—862no—
418#95—862no—
419#95—864no—
420#95—862no—
421#95—864no—
422#95—1722no—
423#95—1722no—
424#95—1722no—
425#95C4×D4314yescomplemented
426C24—432no—
427C24—432no—
428C24—432no—
429C24—434no—
430C24—434no—
431C24—861no—
432C24—861no—
433C24—861no—
434C24—861no—
435C24—862no—
436C24—862no—
437C24C23×D4311yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—432no—
462C22×C4—432no—
463C22×C4—432no—
464C22×C4—4316no—
465C22×C4—434no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—868no—
469C22×C4—868no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—862no—
481C22×C4—861no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—1728no—
494C22×C4—1724no—
495C22×C4—1724no—
496C22×C4—1728no—
497C22×C4—1728no—
498C22×C4—1728no—
499C22×C4—1728no—
500C22×C4—1728no—
501C22×C4—1724no—
502C22×C4—1724no—
503C22×C4—1724no—
504C22×C4—1724no—
505C22×C4C2×C4×D4314yes—
506C22×C4C2×C4×D4312yes—
507C22×C4D4×D4312yes—
508C22×C4#1062190012yes—
509C22×C4Q8×D4312yes—
510C22×C4#1062190212yes—
511C4⋊C4—44no—
512C4⋊C4—1724no—
513C22⋊C4—8616no—
514C22⋊C4—1728no—
515C42—1728no—
516C23—434no—
517C23—438no—
518C23—434no—
519C23—434no—
520C23—438no—
521C23—864no—
522C23—864no—
523C23—864no—
524C23—864no—
525C23—864no—
526C23—864no—
527C23—864no—
528C23—864no—
529C23—862no—
530C23—862no—
531C23—864no—
532C23—862no—
533C23—862no—
534C23—862no—
535C23—862no—
536C23—862no—
537C23—862no—
538C23—864no—
539C23C22×C4×D4311yescharacteristic
540C23C2×D4×D4311yescharacteristic
541C23C2×Q8×D4311yescharacteristic
542C23#41×D4312yes—
543C23#41×D4311yescharacteristic
544C23#41×D4311yescharacteristic
545C23#41×D4312yes—
546C23C2×#1062190011yescharacteristic
547C23C2×#1062190211yescharacteristic
548C23#1306337012yes—
549C23#1306337112yes—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—434no—
579C2×C4—864no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—864no—
583C2×C4—864no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—864no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—17216no—
591C2×C4—17216no—
592C2×C4—17216no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4C4⋊C4×D4314yes—
611C22—438no—
612C22—864no—
613C22—864no—
614C22—864no—
615C22—864no—
616C22—868no—
617C22—864no—
618C22—868no—
619C22—864no—
620C22—868no—
621C22—868no—
622C22C2×C4⋊C4×D4311yescharacteristic
623C22#117×D4312yes—
624C22C4×#1062190011yescharacteristic
625C22C4×#1062190211yescharacteristic
626C22#1458337112yes—
627C22#1458340911yescharacteristic
628C22#1458341211yescharacteristic
629C22#124×D4311yescharacteristic
630C22#124×D4311yescharacteristic
631C22#125×D4312yes—
632C22#1458345411yescharacteristic
633C22#1458345511yescharacteristic
634C22#1458345911yescharacteristic
635C22#1458346011yescharacteristic
636C22#1458352412yes—
637C22#1458357212yes—
638C22#1458357412yes—
639C22#1458357612yes—
640C22#1458357912yes—
641C22#1458359412yes—
642C22#1458359612yes—
643C22#1458360012yes—
644C22#1458360212yes—
645C4—24no—
646C4—42no—
647C4—42no—
648C4—44no—
649C4—82no—
650C4—864no—
651C4—3442no—
652C4—1722no—
653C4—1722no—
654C4—1724no—
655C2—868no—
656C2#382×D4311yescharacteristic
657C2#1913707611yescharacteristic
658C2#1913720611yescharacteristic
659C2#1913753012yes—
660C2#1913753412yes—
661C2#1913974711yescharacteristic
662C2#1913974911yescharacteristic
663C2#1913981312yes—
664C2#1913981512yes—
665C2#1914006911yescharacteristic
666C2#1914007111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1442D43
hypocenterC43#13966
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #19132854C2semidirect
5. #19132852C2semidirect
6. #19132851C2semidirect
7. #19132820C2semidirect
8. #19132819C2semidirect
11. C43×#1442C2semidirect
20. #14582746C4semidirect
69. C2×C4×Dic43C2×C4semidirect
80. C43⋊#95C2×C4semidirect
91. #95×C43C2×C4semidirect
328. #1442D43semidirect
371. C43#13966semidirect
425. #95C4×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145827562
C2×#145827462
C2×#95×D432
#191328542
#191328522
#191328512
#191328202
#191328192
(C2×D43)⋊#952
C43×#14422
#1396643